K-MOND (with "Dark Matter" as a distinction between Inertial and Gravitational Mass)

TL;DR

This paper demonstrates that Milgrom's MOND can be interpreted as a modified kinetic theory, called k-MOND, which introduces a functional dependence between inertial and gravitational mass, resembling dark matter effects at low accelerations.

Contribution

It proposes a new interpretation of MOND as a kinetic modification with a mass distinction, without altering gravitational potential energy terms.

Findings

k-MOND reproduces MOND behavior at low accelerations

Functional dependence between inertial and gravitational mass is established

Dark matter effects are modeled through mass distinction in k-MOND

Abstract

In this work we definitely prove a possibility that Milgrom's modified Newtonian dynamics, MOND, can be consistently interpreted as a theory with the modified kinetic terms of the usual Newtonain dynamics, simply called k-MOND. Precisely, we suggest only a functional dependence between inertial and gravitational mass tending toward identity in the limit of large accelerations (characteristic for Newtonian dynamics and its relativistic generalizations) but which behaves as a principal non-identity in the limit of small accelerations (smaller than Milgrom's acceleration constant). This functional dependence implies a generalization of the kinetic terms (without any change of the gravitational potential energy terms) in the usual Newtonain dynamics including generalization of corresponding Lagrange formalism. Such generalized dynamics, k-MOND, is identical to Milgrom's MOND. Also, mentioned k-MOND distinction between inertial and gravitational mass would be formally treated as "dark matter".